About Me

I'm a Visiting Professor of Philosophy at the University of Ulsan in South Korea. I successfully defended my PhD dissertation ("Truth is a One-Player Game: A Defense of Monaletheism and Classical Logic") last March. I also have an MFA in Creative Writing from the Stonecoast program in Maine. Oh, and I go out at night to fight crime, under the alias "the Caped Logician."
Actually, that last sentence was a lie. (As is this one.) But, according to some people, I am an enemy of "Christendom."

Wednesday, April 27, 2011

I just gave a talk at the National University of Singapore, entitled "Liar Paradox II: Revenge of the Liar Paradox." Singapore, by the way, is lovely, and I'm going to be sorry to leave on Thursday. On the surface it feels enough like Miami to make me feel nostalgic--humid, windy, full of palm trees and outdoor bars and a mishmash of different languages and cultures--while having a lot of appealing un-Miami-ish traits, like being chock-full of restaurants serving delicious Indian food. (The strangest thing I've seen here to date has been Haw Par Villa, a "moral instruction" theme park based on Confucianism and Chinese mythology put up by some early-twentieth-century Chinese millionaires who'd made a killing in the tiger balm trade. The main attraction is the Ten Courts of Hell, where lurid statues and signs depict the punishments sinners are sentenced to by the Emperors of Hell. For example, "cheating on examinations" gets you your intestines ripped out by demons.) While I've been in Singapore, I've been staying with NUS prof Neil Sinhababu, of Possible Girls fame, who will henceforth always have a special place in my heart for saying, when I came in on Saturday night, "I made sure to save some Laphroaig for your visit."

As far as the talk itself, here's the abstract:

Dialetheists like Graham Priest and JC Beall conclude from the Liar Paradox that sentences like “This sentence is not true” are fact both true and untrue, and that we must therefore revise our logic to accommodate the existence of true contradictions. Similarly, “paracomplete” theorists like Hartry Field avoid the contradiction posed by the Liar Paradox by rejecting one of the central elements of classical logic, the Law of the Excluded Middle. A more conservative solution starts from the claim that sentences that attempt to attribute truth or untruth to themselves are meaningless, and therefore simply not the kinds of things we can logically symbolize or apply truth talk to without committing a nonsensical category mistake. The most common objections to this move are (1) that the “meaninglessness solution” is refuted by the existence of “revenge paradoxes” like the one revolving around the sentence “This sentence is either false or meaningless”, and that (2) the sentences involved are so obviously meaningful that it’s just not possible to take seriously the claim that they’re literally meaningless in any ordinary sense, like “Blorks geblork” or “Colorless green ideas sleep furiously,” whereas the dialetheist and paracomplete approaches have the advantages that they (1*) make room for the perfectly obvious fact that, in any language with normal expressive resources, we can construct perfectly meaningful sentences that attribute untruth to themselves, and (2*) are immune to refutation by means of “revenge paradoxes.” I will argue that (1), (2), (1*) and (2*) are all completely wrong.

In terms of the talk itself, I'm never 100% sure what to think about the ethics of blogging in-person discussions, given that I'm sure I wouldn't want to be represented by someone else's half-clear recollection of what I said on the spur of the moment, so I'll pretty well stick to representing what I said myself, with one exception (one hopes, a benign one): In the talk, I spent a few minutes hammering the standard Priest/Beall/Field sort line on Curry's Paradox. In the Q&A, NUS prof Ben Blumson took issue with some of that, and later in the day I ended up spending a couple of hours in his office genially arguing about Curry and related issues, and if I'm still not utterly convinced, I will definitely say that he did a better job of presenting a fairly plausible defense of the approach to Curry I was criticizing than any other defense of that approach I've seen or read before, and in future I will be scaling back at least some of my initial objections in light of some of the points he made.*

In any case, Curry aside, a lot of the ground I covered should be familiar to regular readers here. While I briefly presented my disquotationalist argument for the claim that ungrounded truth talk is literally meaningless, including the Greenness Paradox as a way of defusing the worry that, since we are able to reason about the Liar, we know what follows from it, thus what it means and thus that it means something, my main focus was on revenge paradoxes. (A paper I'm working on making some of these points is tentatively entitled 'Who Among Us Is Safest From The Liar's Revenge?') Conventional wisdom says that the dialetheist and paracomplete approaches to the Liar, given their willingness to engage in radical surgery to our basic logical notions, gain immunity from the revenge paradoxes that typically plague classical solutions to the paradoxes, of which a particularly clear case is supposed to be the problem posed by (1) for those of us who take these sentences to be meaningless:

(1) Sentence (1) is either false or meaningless.

Since paracompletists don't assert anything about the semantic status of such sentences, but rather reject the relevant instances of Excluded Middle, reject the negation of those instances and so on 'all the way down the line,' they seem to be immune from danger from sentences that attribute to themselves the status paracompletists attribute to such sentences. Even more so, dialetheists seem to be immune from any revenge problems, because any 'revenge' liar would at worst just generate yet another true contradiction, and true contradictions don't generate triviality, given the dialetheist's claim that Disjunctive Syllogism isn't universally truth-preserving.

My claim is that (1) is not a problem for the meaninglessness solution at all. A meaningless sentence does not become meaningful once we attach the word "or" to it and paste (what would otherwise be) a meaningful sentence to its tail. Just because a meaningless sentence has the syntactic form of a disjunction and a true second disjunct does not mean that it's meaningful, much less true.

On the other hand, I argue that the paracompletist has a real problem about sentence (2) and that the dialetheist has a real problem about sentence (3).

(2) An ideally rational being who did not lack any relevant information would not accept sentence (2).

(3) It is not the case that sentence (3) is related to truth.

Regular readers will recognize that (2) is the latest form of a revenge paradox for paracompletism I've been tinkering with for some time. The problem, as I see it, is that, if (2) is true, we have the starkly counter-intuitive result that an ideally rational being would not accept a sentence it knew to be true, if (2) is false, we have the equally counter-intuitive result that an ideally rational being would accept a sentence it knew to be false, and if (2) is one of the sentences about which the most rational option is to 'go paracomplete' and reject both the sentence and its negation, then its a sentence that any ideally rational being would not accept (it would reject the sentence instead of accepting it!) and the sentence is true, and, once again, we have the conclusion that an ideally rational being would fail to accept a sentence it knew to be true.

(3) is a familiar problem, but as I argued here, the exact nature of the biggest problem it poses doesn't seem to be widely realized. If being-related-to-truth and not-being-related-to-truth overlap, just as being-related-to-truth and being-related-to-falsehood overlap, then when the dialetheist shows that (given the assumption of dialetheism) there are cases in which all the premises of Disjunctive Syllogism are related to truth and the conclusion is not, they have no more shown that DS is not universally truth-preserving than they would if they'd 'just' showed that all the premises of DS were true and the conclusion was false. No one thinks that "all the premises of argument A are true and the conclusion is false" is a dialetheistically-acceptable way of establishing a failure of truth-preservation. Why should "all the premises of A are related to truth and the conclusion is not" be even a little bit different? Without a better answer to that question, the dialetheist claim that Liars can be both true and false without triviality following simply doesn't hold up.

*On a similar note, I should include a quick shout-out to Brandon Watson for giving me a hard time recently about my error theory about the mistakenness of ordinary competent speakers who take Liars to be meaningful. My preferred way of putting the point now, which I used in the talk, goes about like this: Self-referential sentences are often meaningful--e.g. 'This sentence has seven words in it'--and sentences with precisely the same wording as the Liar sentence are meaningful in other context--'This sentence is false' said while pointing at a sentence about some substantive subject written on a chalkboard. To realize that it's meaningless when the intended reference of the 'this' is that very sentence is a conclusion that takes careful philosophical argumentation. Given those two facts, its quite natural that most people don't realize that it's true. By analogy, if an object is far away and looks a certain (misleading) way from a great distance, and out of a whole crowd of people watching the object, only Bob has a telescope, it's utterly unsurprising that most competent-users-of-functioning-human-eyes end up having a mistaken impression about the object. All Bob needs to do by way of explanation of the disconnect is to say, "yeah, you don't have a telescope. But, hey, look through it yourselves and you'll see where you went wrong here."

Sunday, April 24, 2011

I've argued that, if (as I think) the truth predicate/operator is just a device used to assert things (just as the falsehood predicate/operator is just a device used to assert their negations), it can pretty clearly only be meaningfully applied when there is something there to be asserted--thus, it can only be meaningfully applied to claims about something other than truth. Thus, for example, in a Yablo-like series of sentences where each sentence ascribes truth to the next sentence in the series,

T1: T2 is true.T2: T3 is true.T3: T4 is true.

....and so on forever, all the sentences in the infinite series are literally as devoid of meaning as strings of nonsense syllables, or 'Colorless green ideas sleep furiously.' If, on the other hand, sentence T1000000 is "Snow is white," the rest of the sentences inherit their meanings (and, thus, truth-values) from that.

A semantic property pretty clearly *unlike* truth in this respect is meaningfulness itself. If the meaningfulness predicate only applied to meaningful sentences, it wouldn't fulfill its sole communicative function of separating out the meaningful sentences from the meaningless ones. This is important when we consider (18), which, by analogy to the Liar, we can call The Babbler:

(18) Sentence (18) is meaningless.

If (18) is true, it's both true and meaningless, therefore both meaningful and meaningless, and, of course, if it's meaningless, it's both true and meaningless, therefore both meaningful and meaningless. As such, on pain of contradiction, (18) had better just be false.

Fortunately, in light of the above, we have a good principled reason to think that this is indeed the case. If the function of the meaningfulness predicate is to separate out the meaningful from the meaningless sentences, it has to apply to all sentences. Therefore, it's meaningful to say of any sentence that it's meaningful or meaningless, regardless of the nature of the sentence we're talking about. As such, if all a sentence does is assert a view about the meaningfulness of some sentence, even itself, there's no reason for it not to be meaningful. Thus, (18) is false and (19):

(19) Sentence (19) is meaningful.

...is true.

One important principle, underlying the whole business of revenge-paradoxology, is worth calling attention to here, since I've been implicitly using it a lot. Given these sorts of examples, or, better yet, cased like (20) and (21):

(20) This sentence has seven words in it.(21) This sentence has twenty words in it.

....where it would be clearly absurd to assert about sentence (20), for example, that is seven words long, without granting that sentence (21) is true, we have what we can call the Meaningfulness of Self-Reference Principle: "If Sentence X has property Y, and Sentence X *states* that Sentence X has property Y, then Sentence X is true (and thus, of course, meaningful)."

With all that in mind, and the demonstrations in Parts II and III that it clearly is possible to engage in apparent reasoning about even the most clearly meaningless sentences--meaning that it's not a problem for meaninglessness solutions to the Liar that it's "clearly possible to reason about it, and we all know what does and doesn't follow from it"--let's turn to the apparently troubling revenge paradox for my view that I ended with last time:

(17) Sentence (17) is one that one would have to ultimately label as "false" if one treated it as being meaningful and went through the motions of "reasoning" about it without making the sort of mistake we would regard in normal contexts as a mistake in reasoning.

So, playing along with the game of treating it as meaningful for a moment, an obvious first question is this:

Does (17) take a stand on the question of its own meaningfulness? In other words, does it (a) say of itself that it's meaningful, (b) say of itself that it's meaningless, or (c) remain neutral on that topic?

The wording strongly suggests that (a) would be the wrong gloss--talk of treating it 'as meaningful' and 'going through the motions' strongly suggests that the point is to, at the very least, keep open the possibility that it's meaningless, if not to actively assert it. That said, if (a) is right--it's taking a stand on its own meaningfulness in the directing of asserting it--then to say that, if one went through the motions of reasoning about it, one would make something we would regard in other contexts--i.e. really reasoning about meaningful things--as a mistake, is to say that, if one reasoned about it and failed to come to the conclusion that it was false, one would be making a real, full-fledged mistake in reasoning--a factual mistake, landing us with the wrong answer. In other words, given (a), (17) is just a normal if un-usually phrased Liar sentence, the normal meaninglesness solution applies to it, and the Principle of the Meaningfulness of Self-Reference is not violated if we simultanneously say of it that, although meaningless, going through the motions seems to get us the result that it's false (and true), given that what it's saying is that this isn't a matter of going through the motions in an empty context, because it really is false. (It can be neutral about its own falsehood, given that it asserts its own meaningfulness and thus converts the neutral-sounding language about apparent mistakes into, in effect, the positive claim that one would be making a substantive mistake and getting the wrong result.)

If (b) is the case, then we have a disguised conjunction of two claims: (i) a claim about its alleged meaninglessness, and (ii) a claim about whether any possible analysis of it that (1) took it as meaningful and (2) failed to include any mistakes unrelated to the meaningfulness question would therefore (3) diagnose (17) as false. There's a lot to untangle here, but suffice to say that if it is meaningless, then the true 'first conjunct' asserting as much doesn't make the whole thing meaningful, for reasons examined when we looked at (2), above, and if it's not meaningless, the falsity of the first conjunct guarantees the falsity of the whole thing without fear of contradiction. Really, though, I think the most natural reading is (c), and that's where the real problem seems to be.

If (c) is, then, the case, as should be clear by now, (17) really amounts to a disguised disjunction between the claim that (i*) reasoning about (17) and failing to come to the conclusion that it's false would be a *factual* mistake, and (ii*) that 'reasoning' about (17) leads us to the apparent conclusion that it is false, but only because we're indulging a nonsensical category mistake. In other words, given (c), what we end up with is a disguised version of sentence (2), above:

(2) The sentence marked (2) is either false or meaningless.

...which we already dealt with in Part I. Since I enjoy the circularity of ending by directing back to the first post in the series, I think I'll just leave off there and throw open the floor to questions, comments and devastating objections.

Wednesday, April 13, 2011

A little while ago, I mentioned that I was interviewed for a second appearance on philosophy-oriented podcast Diet Soap. (First one is here.) Anyway, I think the episode with the second appearance on it is going to be coming out within the next couple weeks.

As I emphasized then, I'm happy to be on there. Diet Soap is a podcast I listen to regularly--in fact, lately, it's been the one I've listened to the most regularly that isn't about hockey--and I almost always find it interesting, entertaining and thought-provoking. You should listen.

Anyway, despite having been a normal weekly listener for most of the last bunch of weeks, I somehow missed Episode 91, which was (among other things) about Deluze. Since the most recent episode was a different perspective on Deluze, and the show notes referred to the previous one, I thought I might as well go back and listen to the first Deluze discussion.

...most of which was interesting enough, but towards the end, the host and his guest touched on fatalism and free will in a way that made me want to rip my iPod out of my ears and throw it against the nearest wall in frustration. (I didn't. It's an expensive iPod--one of those tiny little "nano touch" thingies--and what with me being in Korea and all, it'd be even more expensive to replace. Plus, of course, despite my frustration on this particular point, I was still interested to hear the rest of what they had to say.) I've touched on this complaint before, after host Doug Lain brought it up in a previous episode, but I want to take another, more careful crack at it here. Here's what I said about it before:

(2) In the discussions about free will and fatalism, there's a lot of running together of two quite distinct claims:

(i) That there are facts about what will happen in the future, such that some statements about the future are true and some are false, and(ii) That some being knows which statements about the future are true and which ones are false.

Clearly (at least given the orthodox assumption that truth is a necessary condition for knowledge), (ii) entails (i), but (i) can absolutely and obviously be true without (ii) being true. By analogy, consider Claim C (about the past, rather than the future):

C: "Alexander the great's maternal grandmother's paternal grandmother accidentally cut her toe on a rock when she was six years old."

C is pretty clearly either true or false. Whatever one thinks about reference failures and all of that (i.e. whether a statement like "the present King of France is bald" is true, false or neither, given that there is no present King of France), Alexander the Great clearly had a maternal grandmother, and she clearly had a paternal grandmother, and at one point she was six years old. During that year, that lady either did accidentally cut her toe on a rock--in which case C is true--or she didn't (in which case the negation of C is true), and none of this is remotely philosophically controversial. Given atheism (and the absence of time machines) no one is in any position to have epistemic access to the fact of the matter here, but no one thinks that there isn't a fact of the matter about this issue. Why on earth should it be any different, re: future facts and the absence of any being with epistemic access to those facts?

(In the comments on that post, a friend of mine who's working on free will for his doctoral dissertation put the point rather more vehemently than I would.)

Expanding a bit now:

Lain expresses the point in terms of "truth claims", which I find slightly confusing, just because it's not terminology that I'm used to, but I think it's fairly clear in context that it just means "claims that are true." (For the sake of simplicitly, let's make that "true statements.") He's responding to Taylor's classic argument for fatalism (the idea that the future is "fixed" in some way that gets in the way of some important intuitive idea of free will). That argument is spelled out formally by Taylor, and Lain is looking for a way out. So far, so good.

On the philosophical substance here, my own very strong view is that (a) there are lots of ways out, even if Lain's favored one is as problematic as I think it is, but that (b) no matter what your favorite conception is of free will, "fatalism" shouldn't be a problem. We can come back to that in a bit. Meanwhile....

Lain's move is, basically, to leverage atheism against fatalism. If Taylor's picture has it that there is an infinite set of every true statement about the future--and therefore that, for every prediction you could make about the future, either its in that set or its not, but one way or the other, there's a fixed fact of the matter about whether the prediction's going to come true--Lain wants to dispute the claim that there is such a set of true statements. After all, in the absence of an omniscient God, no one is in a position to claim all the infinitely many true things about the future.

In his most recent statement of all this, in Episode 91, Lain made a special point of saying that something can only be a statement if someone has said it, written it down or thought it. I think this might have been a way of side-stepping the way I'd previously expressed my objection, quoted above--in terms of "some statements being true and others being false" vs. "some entity being in a position to know which statements are true and which are false"--and I guess it does, but in a way that I think misses the point.

Think about the past. That's definitely "fixed" and at this point unchangeable in just the sense that anyone worried about fatalism is worried that the future is "fixed", right? Well, even if the past is finite (different physical cosmologies have importantly different results on that point), in a universe without any God-like entities, surely no one is in any position to know, or state, every true statement about the past, right? That is, however, just obviously utterly irrelevant to the pasts' "fixed"-ness.

The reason its irrelevant is that the issue isn't so much about statements as it is about facts. Even if I hadn't come up with the particular example I used in the comments--C: "Alexander the great's maternal grandmother's paternal grandmother accidentally cut her toe on a rock when she was six years old."--and indeed if no one had ever said or thought of that statement (as is extremely likely that no one would have) the lady in question, and all events in her life, would still exist, and either include or fail to include the described incident. Even if one thinks that sentences per se rather, than say, propositions, are the only things that can be "true" or "false", and even if a sentence describing the incident doesn't exist, either the incident occurred or it didn't.

Now, one could make a really radical move here and just deny the existence of un-described facts--if no one has ever commented on or thought about the number of empty bottles on the floor of the basement of the frat house, then there isn't a certain, definite, objective number of bottles there!--and that would sort-of-help here, but, in the end, it wouldn't help much. Not only would this move distance you so much from any remotely recognizable sense of the meaning of the word "truth" as it's used pre-philosophically in ordinary everyday conversations that it's no longer clear to me what we're talking about when we talk about whether some statement is "true" or "false", but even if we make this move, it won't get us off the fatalist hook.

For one thing, we can always reconstruct the fatalistic stuff in terms of hypothetical statements--e.g. "for any possible future event, if one were to make a prediction about it, that prediction would either be a true prediction or it wouldn't be"--and for another, even if we couldn't (and, again, we pretty clearly can), that wouldn't matter very much.

Here's why:

Forget "the future" as a vast (possibly infinitely extended) category, and re-ask yourself why you're concerned with fatalism in the first place. Presumably, it's because we want to think we have the power to change things with our idividual or collective choices, or at the very least that (even if we don't think it's a matter of choice) certain future possibilities we care about are still "open."

The problem is that, for any given future possibility we care about the openness of, we can just construct a sentence about it. For example:

"Doug Lain's great-grandchildren will live under precisely the sort of anarchist-socialist utopia he advocates."

or

"An anarchist-socialist utopia will never come about."

or

"Doug Lain will murder someone on July 15th, 2058, and be executed for that crime."

or

"Doug Lain will never kill anyone."

....or whatever. Whether or not there's an infinite set of true statements for any of these these statements to be part of (if any of them are true) or to be fail to be part of, we hardly need an infinite, omniscient mind for these particular statements to exist. (Check them out! I just wrote them up!) Given that they exist, they're either true or they're not, which is presumably just as much (or, of course, just as little) of a problem for the "openness" or undecidness or whatever of these future possibilities as them being or not being part of some infinite set of true statements would be.

Now, like I said earlier, I tend to think that both (a) if one thinks that its important to avoid this fatalistic result, there are plenty of moves you could make that do so, even if the move under consideration has prospects as dim as I think they are, and that (b) it's actually not important to avoid it (the future is every bit as much "up to us" and to our free choices with or without the kind of 'openness' anti-fatalists tend to be concerned with). That is, though, as they say, a-whole-nother discussion, and one probably best reserved for a blog post of its own, this one being as long as it is already.

So let's do that in a couple weeks. Meanwhile, stay tuned for the long-delayed Part IV of the Liar Pardox posts next Wednesday!

Wednesday, April 6, 2011

My view is that, as my boy Willard Van put it, truth is disquotation. When I prefix the words 'it's true that' to a quoted sentence, the effect of what I've done is to remove the quotation marks. Moreover, I see no principled distinction between this way of ascribing truth to a sentence (quoting it within the larger sentence in which one applies the truth operator to it), or other standard ways of ascribing truth, like saying "that's true" in response to someone else's statement, or the more formal device of writing down a pair of numbered sentences like (14) and (15):

(14) Snow is white.(15) Sentence (14) is true.

In all of these, the function of the truth predicate/operator is exactly the same.

A good analogy in contemporary informal English is "What he said."

Imagine the following, fairly mundane interaction:

An evolutionary biologist, Jane, is drinking at a bar with her boyfriend John (a humanities major with a shaky but more or less accurate grasp on her field) and her loveable-but-frustrating cousin Jack, a fundamentalist Christian (who's just ordering coca cola and bar nachos while his heathen cousin and the man she's living in sin booze up). At some point, Jack brings up evolution and runs through some creationist talking point about missing links in the fossil record or some such. Jane sighs, orders another drink and carefully runs through the scientific explanation of what Jack's talking about. In the end, both cousins stop talking and turn to John, who just tilts his head towards his girlfriend and says "What she said."

This is a normal and immediately familiar usage--note, BTW, that John's sentence isn't syntactically "well-formed", but it's meaningful all the same, "well-formed"-ness in natural language contexts not being necessary for, sufficient for, or even especially relevant t meaningfulness--and we all get what's going on here. "What she said" is a linguistic device John is using as a shorthand method of asserting exactly what Jane just asserted. He could be using it for a variety of reasons--most obviously, using this handy abbreviation is far easier than repeating the entire explanation Jane just gave, but it could also (in this case quite plausibly) be that he doesn't remember every detail of what he means to be asserting. Certainly, there's very little temptation here to think that John means anything above and beyond, or different from, what Jane said. The point of the phrasing is, in fact, to draw attention to the fact that he means to say exactly what, well, "she said."

The word 'true' has various advantages over its functionally kindred linguistic device 'what she said'--for one thing, one can use it on written sentences, and more tellingly, on sentences whose source is unclear--but the point, I think, is the same. Instances of "what she said" are presumably meaningful if the sentence it's applied to are meaningful and meaningless otherwise (John: "Colorless green ideas sleep furiously", Jane: "What he said"), and the same goes, I would argue for truth. The general principle is that truth talk is only *parasitically* meaningful. Prefixing "it's true that" to a *quoted* sentence has the effect of removing the quotation marks--i.e. "it's true that 'snow is white'" means precisely the same thing as "snow is white"--but putting "it's true that" at the beginning of a sentence already outside of quotation marks has no semantic impact at all. (It might add emphasis, but it doesn't change the meaning.) "(16) is true" has no independent meaning not supplied by whatever sentence (16) means. An obvious consequence of this view is that if "(16) is true" inherits no meaning from sentence (16), then it means nothing at all. Hence, if sentence (16) is "snow is white", "(16) is true" does nothing but attribute whiteness to snow, and if (16) is (16) is true, it means nothing at all. Putting a "not" in the mix is never, of course, enough to change a meaningless jumble of words into a meaningful one.

At the end of Part I, I considered one of the most worrying objections to this position. Isn't it manifestly possible to 'reason' about these sentences? Doesn't someone like me, who takes Liar sentences to be meaningless, come to this position on the basis of careful consideration of various other approaches to the paradox? Isn't part of the process of arguing for this solution going to be a matter of arguing against competing solutions, and won't that, in turn, be to a considerable extent a matter of arguing about "what follows" from various Liar sentences, in combination with added premises taken from a proposed solution? (For example: "You say that standard Liar sentences are meaningful but that they do not express propositions. What, then, about a sentence that says of itself that it does not express a true proposition? Surely, if it doesn't express a proposition at all, it doesn't express a true one, right?" or "I don't see how a gap theorist can get around the revenge paradox about a sentence that says of itself that it's either false or gappy" or "How does the dialetheist deal with a sentence that says of itself that it is just false and not true?") If one plays this game as well as anyone, doesn't that show that, like everyone else one grasps the meaning of the sentences in question? After all, isn't this game of generating unappetizing inferences from alternate solutions a matter of drawing out the entailments of the content of these sentences?

In Part II, I responded to this objection by pointing out that the same problem could arise for sentences that everyone takes to be meaningless, drawing out a scenario in which many people might infer contradictions from the sentence "Colorless green ideas sleep furiously" and ways that the hypothetical philosophical debate about this "Greenness Paradox" could closely mimic the actual philosophical debate about the Liar Paradox.

One possible problem here might have to do with distinctions among meaningless sentences. In the comments on Part I, ParisW suggested that there might be quantitative degrees of, or qualitatively different types of meaningfulness, and that different meaningless sentences might interact with logic in different ways. Now, I don't words in his mouth, and the line of thought would have to be developed a bit first anyway, but the general idea could be that it's not legitimate to pick out a meaningless sentence, show how it interacts with logic, and make sweeping generalizations about how Liars interact with logic or fail to do so if they are meaningless.

Now, personally I have trouble seeing how this could get off the ground--"means something"/"means nothing" look pretty clearly binary to me--but maybe the possibility of the "Greenness Paradox" is a consequence of "Colorless green ideas sleep furiously", despite its distinguished history as a stock example of a meaningless sentence, just isn't meaningless enough. How about "blorks geblork"? We could have the following conversation:

Person 1: "Blorks geblork!"Person 2: "That's false."Person 1: "So you think blorks don't geblork?"Person 3: "That doesn't follow from what 2's point that it's not the case that blorks geblork. It could be that there are no blorks."

Clearly, there's something absurd about these three people going through the motions of reasoning about a combination of nonsense syllables. Equally, clearly, Person 1's gloss on Person 2's statement commits some sort of further mistake, correctly highlighted by Person 3's comment, and this further mistake is something that goes above beyond the basic category mistake of applying truth talk to a meaningless string of nonsense syllables and going on to "reason" about them.

Again, one might think this has something to do with degrees or kinds of meaninglessness. The string of nonsense syllables in question, after all, still has an apparent subject-predicate form, which is the entry point for all this.

Take a different example. Let's say I just sneezed. I've made a sound that doesn't sound at all subject-predicate-ish, and that no one who heard it and understood what it was would mistake for a claim about anything. Now, if some strange person did say that my sneeze was "true", a tempting way to correct them would be to say, "no no no, it wasn't true or false. Sneezes are just the wrong kind of thing to be able to count as either."

Once we combine a natural way of symbolizing the first sentence of my "correction" with two banally orthodox assumptions about truth and logic, we have all the ingredients of what we can call the Sneeze Paradox:

By a series of relative simple steps I'll leave as an exercise for the reader, we get to:

Conclusion: S & ~S

One could imagine an (unlikely) scenario where no one ever figured out what was wrong here, and dialetheists used the Sneeze Paradox to argue for true contradictions, gap theorists used it to argue against Bivalence, sophisticated logicians with mostly orthodox premises found all kinds of ingenious ways of twiddling with or conceptually re-thinking the rational role of the logical architecture to avoid the conclusion and so on. Inevitably, various participants in this debate would make various reasoning mistakes.

Of course, we know that the at-bottom mistake underlying the whole debate is a nonsensical category mistake, not a factual mistake of any kind. If my statement "my sneeze wasn't true or false" is true, it's because I don't mean to literally assert the negation of the disjunction of the claim that it is true and the claim that it is false. If I'm talking sense in any sense, it's because what I really mean by the sloppy shorthand "it's not true or false" is "it's not the kind of thing to which 'true' and 'false' can be meaninfully applied, which is a different kettle of fish entirely. Still, on he way to realizing this, we'd doubtless want to nit-pick the arguments of the normal participants in the debate, catch them out on 'errors.'

So, how can we possibly conceptualize these 'errors'? And won't any analysis we give of the nature of these apparent "errors in reasoning" inevitably spawn new revenge problems for the meaningless solution, along the lines of (17)?

(17) Sentence (17) is one that one would have to ultimately label as "false" if one treated it as being meaningful and went through the motions of "reasoning" about it without making the sort of mistake we would regard in normal contexts as a mistake in reasoning.

To which all I can say is, stay tuned for the exciting conclusion of our quadrilogy to find out!

Monday, April 4, 2011

Three weeks from tomorrow, I'll be delivering a talk at the Philosophy Department at the National University of Singapore (NUS) entitled "Liar Paradox II: Revenge of the Liar Paradox." In lieu of Part III of the ongoing series on the same subject, here's the abstract I sent them for the talk (and then a quick explanation of where I'm going with it):

Dialetheists like Graham Priest and JC Beall conclude from the Liar Paradox that sentences like “This sentence is not true” are fact both true and untrue, and that we must therefore revise our logic to accommodate the existence of true contradictions. Similarly, “paracomplete” theorists like Hartry Field avoid the contradiction posed by the Liar Paradox by rejecting one of the central elements of classical logic, the Law of the Excluded Middle. A more conservative solution starts from the claim that sentences that attempt to attribute truth or untruth to themselves are meaningless, and therefore simply not the kinds of things we can logically symbolize or apply truth talk to without committing a nonsensical category mistake. The most common objections to this move are (1) that the “meaninglessness solution” is refuted by the existence of “revenge paradoxes” like the one revolving around the sentence “This sentence is either false or meaningless”, and that (2) the sentences involved are so obviously meaningful that it’s just not possible to take seriously the claim that they’re literally meaningless in any ordinary sense, like “Blorks geblork” or “Colorless green ideas sleep furiously,” whereas the dialetheist and paracomplete approaches have the advantages that they (1*) make room for the perfectly obvious fact that, in any language with normal expressive resources, we can construct perfectly meaningful sentences that attribute untruth to themselves, and (2*) are immune to refutation by means of “revenge paradoxes.” I will argue that (1), (2), (1*) and (2*) are all completely wrong.

#

On (2)/(1), of course, see Part I and Part II of the series of posts I've been doing on that here. (And, of course, stay tuned for Part III on Wednesday!) To get a sense of what I'm talking about on (1)/(2*), see (on the paracomplete side) here. On the dialetheist side, the problem, as I see it, is this*:

The dialetheist wants to argue that Disjunctive Syllogism fails to be universally truth-preserving (given true contradictions), and so it cannot be used to infer triviality after the dialetheist has embraced the contradictions entailed by the various paradoxes.

What does it mean to fail to be universally truth-preserving?

Given logical orthodoxy, the obvious answer is that an inference fails to be universally truth preserving iff there are possibilities on which the premises are all true and the conclusion is false. The dialetheist, obviously, can't conceive of it that way. Given the possibility of true contradictions, we can have possibilities where the premises of an argument are all true and the conclusion is false....but also true. On dialetheist assumptions, the mere fact that we've inferred a false conclusion from true premises is insufficient to establish that the the inference form fails to be universally truth-preserving.

Graham Priest's solution is to conceive of failures-of-truth-preservation as cases where the premises all 'relate to truth' and the conclusion fails to do so. (For technical reasons of his own, he prefers to think of truth as a relation rather than a function--so sentences 'relate' to truth or 'relate' to falsehood or both--but that's not really relevant right now. Talk of sentences relating to truth can translate to talk of them being true with no loss of nuance relevant to our discussion here.) The problem is that, obviously, it's always possible to come up with a Liar that says of itself that it fails to relate to truth. If normal Liars establish the possibility of sentences being simultaneously true and false, these anti-dialetheist revenge Liars should equally well establish the possibility of sentences simultaneously relating to truth and failing to relate to truth. Given this, establishing the possibility of all of the premises of an instance of Disjunctive Syllogism relate to truth while the conclusion fails to relate to truth should be not a single bit more relevant to showing that it fails to be universally truth-preserving than establishing the possibility of all the premises of an instance of Disjunctive Syllogism being true while the conclusion is false.

More generally, it looks like for any Status S such that the dialetheist could try to turn to in order to say "an argument fails to be universally truth preserving iff the premises are all true and the conclusion has Status S", we can always construct a revenge Liar of the form "This sentence has Status S" that will, on dialetheist assumptions, establish that true sentences can also have Status S. Once we've established this, it's not clear why Status S is a better candidate for a definition of failures-of-truth-preservation than mere falsity.

Many people have noticed the possibility of such sentences, shredding up distinctions dialetheists seem to find important--e.g. between sentences that are false-and-also-true and those that are "just" false ("This sentence is just false and not true")--and felt that in some way this was a problem for the dialetheist position on the Liar. Graham Priest, at least, has a standard response, found in multiple books and papers. He'll analyze the Liar sentence in question, show how the contradiction is derived from it, show how triviality fails to be entailed by the contradiction in his favored system of paraconsistent logic, and make some variation of a quip about how his point was never to avoid contradictions, but merely to contain them.

The problem, if I'm right about this, is that dialetheism's revenge problems don't just deliver more contradictions, they tear down the bars dialetheists want to use to contain them.